The question consists of three statements numbered 

Solution

Statement I: According to the statement; Balance in the account at the end of two years = Rs. 20,000 Balance in the account at the end of three years = Rs. 25,000 So, P × {1 + (r/100)}² = 20000 --------- (I) And, P × {1 + (r/100)}³ = 25000 --------- (II) On dividing equation (II) by equation (I), we have; {1 + (r/100)} = 25000/20000 Or, {1 + (r/100)} = 5/4 Or, {1 + (r/100)} = 1.25 So, r = 25 So, rate of interest = 25% p.a. On putting r = 25 in equation (I), we have; P × (1.25)² = 20000 Or, P × 1.5625 = 20000 Or, P = 12800 So, data in statement I alone is sufficient to answer the question. Statement II: Let {1 + (r/100)} be x. Therefore, Amount at the end of 3 years = Px³ = 25000 Interest earned during 2nd year = Px² - Px Interest earned during 3rd year = Px³ - Px² According to the statement; (Px³ - Px²) - (Px² - Px) = 1000 Or, Px³ - 2Px² + Px = 1000 Since, Px³ = 25000 So, 25000 - 2Px² + Px = 1000 Or, 2Px² - Px = 24000 Dividing throughout by Px³, we get (2x - 1)/x² = 24000/25000 Or, (2x - 1)/x² = 24/25 Or, 24x² - 50x + 25 = 0 Or, 24x² - 30x - 20x + 25 = 0 Or, 6x(4x - 5) - 5(4x - 5) = 0 Or, (4x - 5)(6x - 5) = 0 Or, x = 5/4, 5/6 Since, at x = 5/6, rate will be negative therefore, x = 5/4 Or, {1 + (r/100)} = 5/4 = 1.25 Or, r/100 = 0.25 Or, r = 25 Since, P{1 + (r/100)}³ = 25000 Or, P{1 + (25/100)}³ = 25000 Or, P × (1.25)³ = 25000 Or, 1.953125P = 25000 Or, P = 12800 So, data in statement II alone is sufficient to answer the question. Statement III: According to the statement; If Rs. P was invested at simple interest of (1.6r)% p.a., then interest earned at the end of 3 years would have been more than the actual interest earned. But from this statement, we cannot determine the exact value of r or P. So, data in statement III alone is not sufficient to answer the question. So, data given either in statement I alone or in statement II alone is sufficient to answer the question while data given in statement III alone is not sufficient to answer the question.